Question

How to show that the beta funcction is well defined?

score 100 · Answer 1 · 2020-06-09 16:17:16

100

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How to show that the beta funcction is well defined?

Published on 09 Jun 2020 - 16:17

score 136 · Answer 2 · 2020-06-11 02:31:21

136

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Show that $\int_{0}^{\pi/2} (\frac{1}{\sin^3{\theta}} - \frac{1}{\sin^2{\theta}})^{1/4} \cos{\theta} d\theta = \frac{(\Gamma(1/4))^2}{2\sqrt{\pi}}$

Published on 11 Jun 2020 - 2:31

score 67 · Answer 3 · 2020-06-15 22:07:58

67

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Big-theta asymptotic limit of expression involving incomplete beta function

Published on 15 Jun 2020 - 22:07

score 54 · Answer 4 · 2020-06-17 04:45:07

54

Views

Is there a way of solving $I_x^{-1}(a_1,b_1)w_1+I_x^{-1}(a_2,b_2)w_2=k$?

Published on 17 Jun 2020 - 4:45

score 268 · Answer 5 · 2020-06-17 21:28:38

268

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What is being done in this Integration by Parts proof of $\int_0^1 x^a(1-x)^b \, dx$?

Published on 17 Jun 2020 - 21:28

score 445 · Answer 6 · 2020-06-19 20:41:49

445

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History of Gamma and Beta functions

Published on 19 Jun 2020 - 20:41

score 121 · Answer 7 · 2020-06-21 16:12:51

121

Views

Series of square of factorial

Published on 21 Jun 2020 - 16:12

score 117 · Answer 8 · 2020-06-22 03:35:03

117

Views

Showing $\sum_{k=0}^{n+1} \binom n k \frac{(-1)^k}{(n+k)(n+k+1)} = \sum_{k=0}^{n+1} \binom {n+1} k \frac{ (-1)^k}{n+k}$

Published on 22 Jun 2020 - 3:35

score 44 · Answer 9 · 2020-06-24 21:05:10

44

Views

Beta - Binomial conjugacy equivalent for 1 - B

Published on 24 Jun 2020 - 21:05

score 54 · Answer 10 · 2020-06-28 17:55:14

54

Views

Why does the beta function look like a Sudoku grid?

Published on 28 Jun 2020 - 17:55

score 88 · Answer 11 · 2020-07-03 19:21:18

88

Views

Simplify integral to beta or gamma function

Published on 03 Jul 2020 - 19:21

score 187 · Answer 12 · 2020-07-04 15:58:26

187

Views

Series with coefficients coming from beta function

Published on 04 Jul 2020 - 15:58

score 75 · Answer 13 · 2020-07-15 11:20:17

75

Views

Does this function has a name? (Similar to Beta Function)

Published on 15 Jul 2020 - 11:20

score 153 · Answer 14 · 2020-07-15 11:58:16

153

Views

Help with Variant of Abel's Integral

Published on 15 Jul 2020 - 11:58

score 640 · Answer 15 · 2020-07-21 07:06:53

640

Views

Integrals related to $\int_0^{\pi} \left(\frac{\sin(\alpha u)^\alpha \sin((1-\alpha) u)^{1-\alpha}}{\sin u} \right)^{\rho/\alpha}du$

Published on 21 Jul 2020 - 7:06

List Question

How to show that the beta funcction is well defined?

Show that $\int_{0}^{\pi/2} (\frac{1}{\sin^3{\theta}} - \frac{1}{\sin^2{\theta}})^{1/4} \cos{\theta} d\theta = \frac{(\Gamma(1/4))^2}{2\sqrt{\pi}}$

Big-theta asymptotic limit of expression involving incomplete beta function

Is there a way of solving $I_x^{-1}(a_1,b_1)w_1+I_x^{-1}(a_2,b_2)w_2=k$?

What is being done in this Integration by Parts proof of $\int_0^1 x^a(1-x)^b \, dx$?

History of Gamma and Beta functions

Series of square of factorial

Showing $\sum_{k=0}^{n+1} \binom n k \frac{(-1)^k}{(n+k)(n+k+1)} = \sum_{k=0}^{n+1} \binom {n+1} k \frac{ (-1)^k}{n+k}$

Beta - Binomial conjugacy equivalent for 1 - B

Why does the beta function look like a Sudoku grid?

Simplify integral to beta or gamma function

Series with coefficients coming from beta function

Does this function has a name? (Similar to Beta Function)

Help with Variant of Abel's Integral

Integrals related to $\int_0^{\pi} \left(\frac{\sin(\alpha u)^\alpha \sin((1-\alpha) u)^{1-\alpha}}{\sin u} \right)^{\rho/\alpha}du$

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